Estimating Hardness of Cosmetic Cream Using Electro-Mechanical Impedance Sensing Technique

Abstract

This study investigates the application of electro-mechanical impedance (EMI) sensing technology to evaluate the hardness of cosmetic creams. Traditional methods, like penetration resistance testing, can be intrusive and disrupt continuous monitoring by impacting internal structures. To overcome this limitation, a piezoelectric sensor is embedded in cosmetic creams to capture EMI signals. This experiment explores varying wax content levels in the creams, establishing correlations between conventional hardness values and EMI signals. The results demonstrate a positive relationship between wax content, hardness values, and the magnitude of EMI resonance peaks. This study emphasizes a robust correlation between established hardness metrics and EMI signals, showcasing the potential of non-destructive testing to drive advancements in cosmetic industry practices.

1. Introduction

The hardness of cosmetics is a pivotal factor directly influencing consumer satisfaction. Specifically, the hardness of cosmetic products, including creams, balms, and lipsticks, holds significant sway over their efficacy. Consumer preferences are often centered around specific textures and consistencies, making the measurement of hardness essential for evaluating a product’s alignment with these expectations. Consumer satisfaction is intricately linked to the sensory experience of using cosmetics, and a dissonance between a product’s hardness and consumer expectations can lead to dissatisfaction and negative brand perceptions. The hardness of cosmetics serves as a key indicator of product quality, ensuring a consistent texture that delivers the desired feel and contributes significantly to a positive consumer experience [1,2].

Moreover, the hardness of cosmetics plays a crucial role as an indicator of manufacturing quality control. Within the realm of cosmetic formulations, which encompass diverse ingredient combinations, hardness measurements are pivotal in optimizing formulations to achieve the desired properties, including texture, spreadability, and adhesion. Additionally, monitoring changes in the hardness of cosmetic products over time serves as an early warning for potential stability issues. Regular hardness assessments enable the proactive identification of problems, such as ingredient separation or degradation, allowing for preemptive measures before they compromise product performance [3].

The most common method to measure cosmetic hardness is penetration resistance testing using a texture analyzer. In this test method, the hardness of cosmetics is evaluated by calculating the stress, which is accomplished by dividing the load when the probe is inserted into the cosmetics at a certain depth and at a certain speed by the cross-sectional area of the probe. This test method has certain advantages, including test equipment that is compact and easy to operate. However, since this test method involves penetrating probes into cosmetics, it destroys the internal structure of the cosmetics. Therefore, there are limitations in continuously measuring the hardness of cosmetics [4,5].

In the construction field, penetration resistance tests, similar to the cosmetics hardness test method, are commonly used to evaluate the hardening properties of cementitious materials [6,7]. Penetration resistance testing for cementitious materials uses the same sample to evaluate hardening over time. Penetration resistance values are measured by inserting the probe at a different location in the same sample [7]. However, the repeated penetration of the probe into different locations of the same sample can lead to a collapse of the internal structure, thereby affecting subsequent penetration.

To overcome these limitations of destructive testing, various non-destructive tests have been proposed to evaluate the hardening of cementitious materials in the construction field [8,9,10,11,12,13,14,15,16,17,18,19]. Lee et al. have proposed an electro-mechanical impedance (EMI) sensing technique using a piezoelectric sensor as a non-destructive test to evaluate the hardening of cementitious materials [20,21,22,23]. In studies by Lee et al., a piezoelectric sensor was directly embedded in a cementitious material and the EMI signal of the piezoelectric sensor was measured continuously over time to evaluate the hardening properties of the cementitious material. The EMI signal of the piezoelectric sensor embedded in the cementitious material undergoes changes corresponding to variations in the rigidity of the cementitious material surrounding the sensor. This enables the determination of the degree of hardening of the cementitious material surrounding the piezoelectric sensor.

In the EMI sensing technique, the impedance of the piezoelectric sensor shows a corresponding change depending on the mechanical properties of the material surrounding the piezoelectric sensor, and the mechanical properties of the material can be inferred through the impedance value of the piezoelectric sensor. When cementitious materials react with water, they initially remain in a fluid state and then undergo a phase transition to a solid state over a certain period of time. In studies conducted by Lee et al. [20,21,22,23], the piezoelectric sensors were used to continuously monitor EMI signals over the hydration time to accurately evaluate the stiffness at the moment of the phase transition from the fluid to the solid state. In this context, assessing the mechanical properties of creams in cosmetics that remain in a fluid state may be simpler than assessing the mechanical properties of cementitious materials undergoing phase transitions. Therefore, it is believed that inferring the hardness of a cosmetic cream by embedding a piezoelectric sensor in the cosmetic cream and measuring the impedance of the piezoelectric sensor will be possible.

In this study, the hardness of cosmetic cream was estimated using the EMI sensing technique. Through the embedding of a piezoelectric sensor in the cosmetic cream, we measured the EMI signal of the piezoelectric sensor. Subsequent analysis was conducted to establish a correlation between the EMI sensing technique and the existing hardness test method, specifically the penetration resistance test using a texture analyzer.

2. Electro-Mechanical Impedance Sensing Technique

EMI sensing technology operates on a straightforward principle. When a piezoelectric sensor is connected to a host structure and subjected to a sinusoidal voltage, vibrations occur in the bonded area of the structure due to the direct influence of the piezoelectric materials. The mechanical impedance of the host structure changes with variations in its mechanical properties, leading to a corresponding change in the electrical impedance of the piezoelectric sensor connected to the host structure. The EMI can be calculated by analyzing the input and output signals of the piezoelectric sensor [24,25,26]. Liang et al. proposed a one-dimensional electro-mechanical interaction model for the piezoelectric sensor surface bonded to the host structure, as depicted in Figure 1 and Equation (1) [26].

$$\mathrm{Y}\left(\omega \right)=j\omega \frac{w_A{l}_A}{h_A}\left[\frac{d_{31}^2{\stackrel{-}{Y}}_{11}^E{Z}_A}{Z_A+Z}{\frac{\mathit{tan}({\mathit{kl}}_A)}{{\mathit{kl}}_A}+{\stackrel{-}{\epsilon }}_{33}^T-d}_{31}^2{\stackrel{-}{Y}}_{11}^E\right]$$

(1)

where Y(ω) represents the electrical admittance of a piezoelectric sensor bonded to a host structure (inverse of impedance), j is the imaginary unit (√(−1)), $\omega$ is the excitation frequency, $w_A$ is the width of the piezoelectric sensor, $l_A$ is the length of the piezoelectric sensor, $h_A$ is the thickness of the piezoelectric sensor, $Z$ is the host structural impedance, $Z_A$ is the impedance of the piezoelectric sensor, $k$ is the wave number, ${\overline{\epsilon }}_{33}^T$ is the dielectric constant of the piezoelectric sensor in a 3–3 direction, $d_{31}$ is the piezoelectric constant, and ${\overline{Y}}_{11}^E$ is the complex Young’s modulus of the piezoelectric sensor. The equation reveals that, as the mechanical impedance of the piezoelectric sensor remains constant over the monitoring period, any change in the mechanical impedance of the host structure directly impacts the electrical impedance measured by the transducer. Consequently, this method facilitates the monitoring of changes in the mechanical impedance of the host material by measuring the electrical impedance of the piezoelectric sensor combined with the host material.

When piezoelectric sensors are embedded in cosmetic creams with different hardness levels, the mechanical impedance of the cosmetic cream undergoes changes influenced by the varying hardness of the cream. The relationship between the mechanical properties of the cosmetic cream, such as hardness, and the corresponding changes in the electro-mechanical impedance measured by the embedded piezoelectric sensors forms the basis for estimating the hardness of the cosmetic creams using the EMI sensing technique.

The objective of this study is to estimate the hardness of cosmetic creams using electro-mechanical impedance (EMI) sensing technology. To achieve this, cosmetic creams with varying hardness levels determined by the wax content are manufactured. A comparative analysis is then conducted, contrasting hardness values obtained through conventional hardness test methods with electro-mechanical impedance values acquired through EMI sensing techniques. The goal is to establish correlations between the two datasets, providing insights into the relationship between wax-content-dependent hardness and EMI signals.

3. Experimental Program

3.1. Materials and Sample Preparation

In this study, a cosmetic base was formulated according to the proportions specified in

Table 1. Manufacturing prescription for cosmetic cream.

Ingredients		Contents (%)
		Plain	2%	4%	6%	8%
A	Distilled water	29.50	27.50	25.50	23.50	21.50
	Glycerin	3	3	3	3	3
	Propylene glycol	3	3	3	3	3
	Triethanolamine	1	1	1	1	1
	1,2-Hexanediol	1	1	1	1	1
B	Distilled water	50	50	50	50	50
	Carbomer 980	1	1	1	1	1
C	Stearic acid	1	1	1	1	1
	Cetyl alcohol	1	1	1	1	1
	Squalane	7	7	7	7	7
	White petrolatum	0.5	0.5	0.5	0.5	0.5
	Polyoxyetylene sorbitan monostearate	2	2	2	2	2
	Beeswax	0	2	4	6	8
Total		100	100	100	100	100

Note: A, water phase; B, thickener phase; and C, oil phase.

. Glycerin and propylene glycol were employed as moisturizers, carbomer 980 served as a thickener, and triethanolamine (TEA) acted as a neutralizer. In the oil phase, surfactant, squalane, white petrolatum, and beeswax were utilized. The emulsion was produced by emulsifying for 5 min at a speed of 3000 rpm using a homo mixer (T.K. Auto Homomixer Mark II, Tokushu Kika Kogyo Co., Ltd., Tokyo, Japan). To examine variations in hardness related to wax content, emulsions were created by adding 0, 2, 4, 6, and 8% of beeswax.

3.2. Test Method

This study aimed to assess the hardness of the cosmetic cream using the EMI sensing technique. A commercially available buzzer-type piezoelectric sensor (model CBC2035BA, Daeyoung Electric Co., Ltd., Gyeongsan, Republic of Korea) was embedded in a cosmetic sample, and the resulting EMI signal was recorded. To prevent short-circuiting within the cosmetics, a thin layer of acrylic resin was applied to the surface of the piezoelectric sensor. Figure 2 and

Table 2. Specification of sensor.

	Frequency (kHz)	Resonant Resistance (Ω)	Capacity (pF)	Dimension (mm)				Plate Material
				D	d	T	t
	3.5 ± 0.5	350	30,000 ± 30	20	15	0.23	0.1	Brass

present the specifications of the piezoelectric sensor used in the study.

In the experimental setup, a piezoelectric sensor coated with acrylic resin was centrally positioned within a cosmetic cream sample with a diameter of 100 mm and a height of 100 mm. After preparing the cosmetic cream, it was poured into a container with a diameter of 100 mm and a height of 100 mm. A piezoelectric sensor coated with acrylic resin was embedded in the center of the container and sealed. Subsequently, the samples were left at a temperature of 21 °C and a relative humidity of 55% for 24 h.

EMI signals were measured using an LCR (inductance (L), capacitance (C), and resistance (R)) meter (3235-50 LCR HiTESTER, Hioki, Dallas, TX, USA), and data were collected through a GP-IB connection linked to the LCR meter. During the EMI test, the LCR meter discharged a sinusoidal AC voltage (1 voltage) to excite the piezoelectric sensor. The frequency range for EMI signal measurement ranged from 20 kHz to 250 kHz, with a frequency interval set at 50 Hz. Figure 3 illustrates the schematic representation of the equipment used for measuring EMI signals in the study.

Figure 4 shows the EMI signal during the free vibration of the piezoelectric sensor coated with acrylic resin in air. The EMI resonance frequency of the piezoelectric sensor is recorded as 130.8 kHz, and the magnitude of the EMI resonance peak is measured at 0.047 siemens. This information provides insight into the behavior of the piezoelectric sensor under free vibration conditions, specifically highlighting the resonance characteristics at the specified frequency.

To validate the EMI sensing technique, a penetration resistance test was performed using a texture analyzer, a conventional method for assessing the hardness of cosmetic creams. After preparing the cosmetic cream, it was sealed in a container with a diameter and height of 100 mm and left at a temperature of 21 °C and a relative humidity of 55% for 24 h. Afterwards, the hardness of the cosmetic cream was measured using a texture analyzer (Sun Rheometer CR-100, Sun Scientific, Tokyo, Japan). The penetration resistance of the cosmetic cream was calculated by dividing the load value when a 15 mm diameter probe penetrated 30 mm into the cosmetic cream by the cross-sectional area of the probe.

4. Results and Discussion

Figure 5 shows the hardness of the cosmetic cream relative to the wax content, as measured using a hardness meter. The corresponding hardness values for cosmetic creams with 0%, 2%, 4%, 6%, and 8% wax content were 0.55 kPa, 0.61 kPa, 0.72 kPa, 0.99 kPa, and 1.6 kPa, respectively. The data indicate a positive correlation between the wax content and the hardness of the cosmetic cream. Regression analysis reveals an exponential relationship, indicating a significant and non-linear growth in hardness as the wax content increases.

In Figure 6, the EMI signals of the piezoelectric sensor embedded in the cosmetic cream are depicted, showcasing variations corresponding to different levels of wax content. Upon embedding the piezoelectric sensor in the cosmetic cream, the EMI resonance frequency remains relatively stable, while the magnitude of the EMI resonance peak notably decreases. The magnitude of the EMI resonance peak of the cosmetic creams with wax contents of 0%, 2%, 4%, 6%, and 8% were 0.0326 siemens, 0.0315 siemens, 0.0306 siemens, 0.0280 siemens, and 0.0260 siemens, respectively. A comparison of the magnitude of the EMI resonance peak during the free vibration of the piezoelectric sensor (Figure 4) to that of the piezoelectric sensor embedded in the cosmetic cream without wax (depicted in Figure 6a) reveals a reduction of approximately 30.6%. This reduction can be explained using Equation (1), where an increase in the mechanical impedance of the material surrounding the piezoelectric sensor leads to a decrease in the admittance magnitude [22,26]. Given that the electro-mechanical properties of the piezoelectric sensor depend on the surrounding materials, the decrease in the resonance peak’s magnitude is attributed to the heightened mechanical impedance of the cosmetic cream within the material surrounding the piezoelectric sensor. This observation suggests the effectiveness of the proposed method in monitoring the increase in hardness (impedance) of materials surrounding the piezoelectric sensor, such as cosmetic creams.

Figure 7 shows the relationship between the wax content of the cosmetic creams and the magnitude of the EMI resonance peaks. With an increase in wax content, there is a noticeable decrease in the magnitude of the EMI resonance peak. This trend suggests that higher wax content in cosmetic cream correlates with increased cream hardness, leading to elevated mechanical impedance around the piezoelectric sensor and a subsequent reduction in the EMI resonance peak of the piezoelectric sensor [22,26]. As the wax content rises, the EMI resonance peak of the piezoelectric sensor decreases linearly. Regression analysis results in a coefficient of determination of 0.96, indicating a robust correlation. This finding supports the notion that changes in wax content directly influence the hardness of cosmetic cream, affecting the mechanical properties around the piezoelectric sensor and, consequently, the recorded EMI signals.

Figure 8 shows the correlation between the hardness values and the resonance peak magnitudes, as determined through a combination of hardness testing and EMI detection techniques. The relationship between the cosmetic cream’s hardness value, determined through the hardness test, and the EMI resonance peak of the piezoelectric sensor within the cosmetic cream obtained through the EMI sensing technique is modeled using a logarithmic function with a substantial coefficient of determination at 0.97, affirming a strong correlation. The logarithmic relationship suggested that the increase in hardness values might have a diminishing effect on the magnitude of the EMI resonance peak, highlighting the intricate nature of the interaction between material hardness and EMI signals.

5. Conclusions

This study investigated the use of EMI sensing technology to estimate the hardness of cosmetic creams. The experimental program involved manufacturing cosmetic creams with different wax content levels and measuring their hardness using traditional methods. Simultaneously, the EMI signals of the piezoelectric sensor embedded in the creams were recorded. The results demonstrated a positive correlation between wax content and both hardness values and the magnitude of the EMI resonance peaks. This study established a strong correlation between traditional hardness values and EMI signals, affirming the effectiveness of the proposed EMI sensing technique in estimating cosmetic cream hardness. The logarithmic relationship between hardness and EMI signals highlighted the interaction between material hardness and electro-mechanical properties.

This study contributes to the exploration of non-destructive testing methods in the cosmetic industry, offering a promising avenue for real-time monitoring of cosmetic properties. The findings provide valuable insights for cosmetic formulation optimization, quality control, and early detection of stability issues.